Problem 3010. Self-similarity 1 - Every other term

Created by goc3

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Self-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the <a href = "https://oeis.org/selfsimilar.html">OEIS page</a> for more information.In this problem, you are to check if the sequence is self-similar by every other term. The problem set assumes that you use the easiest route: take the first element and then every other element thereafter of the original sequence, and compare that result to the first half of the original sequence. The function should return true if the extracted sequence is equal to the first half of the original sequence.For example,<ul><li>seq_original_set = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4]</li><li>seq_every_other = [0, , 1, , 1, , 2, , 1, , 2, , 2, , 3, ,] (extra commas are instructional and should not be in the every-other series)</li><li>seq_orig_first_half = [0, 1, 1, 2, 1, 2, 2, 3]</li></ul>Since seq_every_other = seq_orig_first_half, the set is self-similar.This problem is related to <a href = "https://www.mathworks.com/matlabcentral/cody/problems/3011-self-similarity-2-every-third-term">Problem 3011</a> and <a href = "https://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms">Problem 3012</a>.

Self-similar integer sequences are certain sequences that can be reproduced by extracting a portion of the existing sequence. See the <https://oeis.org/selfsimilar.html OEIS page> for more information.

In this problem, you are to check if the sequence is self-similar by every other term. The problem set assumes that you use the easiest route: take the first element and then every other element thereafter of the original sequence, and compare that result to the first half of the original sequence. The function should return true if the extracted sequence is equal to the first half of the original sequence.

For example,

* seq_original_set = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4]
* seq_every_other = [0,  ,  1, , 1, , 2, , 1, , 2, , 2, , 3, ,] (extra commas are instructional and should not be in the every-other series) 
* seq_orig_first_half = [0, 1, 1, 2, 1, 2, 2, 3]

Since seq_every_other = seq_orig_first_half, the set is self-similar.

This problem is related to <https://www.mathworks.com/matlabcentral/cody/problems/3011-self-similarity-2-every-third-term Problem 3011> and <https://www.mathworks.com/matlabcentral/cody/problems/3012-self-similarity-3-every-other-pair-of-terms Problem 3012>.

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Last Solution submitted on Oct 16, 2022

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Asif Newaz on 22 Feb 2020

what do u mean by every other element?

Rafael S.T. Vieira on 31 Aug 2020

Asif, it means an index like: 1,0,1,0,1,0,1,0 ...

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